A zero-one law of almost sure local extinction for (1+β)-super-Brownian motion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Zhou, Xiaowen

关键词: (1+beta)-super-Brownian motion;    Almost sure local extinction;    Zero-one law;    Historical super-Brownian motion;    Integral test;   

DOI  :  10.1016/j.spa.2007.11.011

来源: Elsevier

【 摘 要 】

This paper considers the following generalized almost sure local extinction for the d-dimensional (1 + beta)-super-Brownian motion X starting from Lebesgue measure on R(d). For any t >= 0 write B(g(t)) for a closed ball in Rd with center at 0 and radius g(t), where g is a nonnegative, nondecreasing and right continuous function on [0, infinity). Let tau := sup{t >= 0 : X(t)(B(g(t))) > 0}. For d beta < 2, it is shown that P{tau = infinity} is equal to either 0 or 1 depending on whether the value of the integral integral(infinity)(1) g(y)(d) y(-1-1/beta) dy is finite or infinite, respectively. An asymptotic upper bound for P{tau > t} is found when P{tau < infinity} = 1. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

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